Previously in printing methods for ink-jet printers, the printer's carriage was moved to the start of print area of a paper sheet, one or more lines was printed in a single pass of the carriage, the carriage was stopped at the end of such lines, the paper sheet was advanced, and the steps were repeated for the next lines. Much time is wasted during such conventional printing process, because of the sequential nature of the various process steps. Prior art printing methods may be summarized as having included numerous steps that were performed consecutively. Of course, the printer's paper sheet cannot be advanced during the printing of a given one or more lines printed during the passage of the printer's carriage without screwing up the printed output. On the other hand, it is desired to speed up the printing process, i.e. it is desired to increase the printer's throughput, by eliminating unnecessary delays or other wasted time. At the same time, any concurrent or overlapped movement of the printer's carriage or paper advance mechanism or firing of the ink-jet printer's ink jets preferably would not increase current demand on the printer's power supply.